3D Trying to create an 80s neon grid landscape

ok, so I don't know how to explain the problem I have right now so instead, I try to show it. I try to create a 3D geometry like the landscape pictured below for some background visuals.


But my current model looks something like this


The left model is a trianglelist with a texture 64x64px with a 1px outline for every two triangles forming a rectangle and the other one is a linelist. Why does the textured model have these gaps in the outlines? Is that normal because of 3D? How do other games achieve a similar effect? I'm a complete noob at these 3D things.

So the question is: How can I make the lines on the textured model as clearly visible as on the linelist model?

Thank you so much for your help! I really appreciate it

Edit: Mip Mapping helped a lot but unfortunately introduced other inconsistencies...
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